ABC26GN5301 · Permutations and Combinations

Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: 2009 · Marks: · Difficulty:

Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

(a)76

(b)80

(c)84

(d)96

(e)None of these

Answer

Answer (as printed): B

Explanation

Required number of ways = (5C1 × 4C2) + (5C2 × 4C1) + (5C3)  4 × 3  5 × 4   5 × 4 × 3 =  5 ×  + × 4 +   2 × 1  2 × 1   3 × 2 × 1  = (30 + 40 + 10) = 80.

Explanation as extracted from the printed page; notation may be imperfect.

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